All that can presently (September 2022) be gleaned about Annie Dunbar (Annie Jane Fairbrother) from sheet music covers and by Internet searching is that she was presumably an English music hall performer who has been featured on just one work namely That's Where the Money Goes (1886) music by Joseph Tabrar, words by Peter Conroy and published by Francis, Day & Hunter, London W.C.2, England
Her portrait on the left is taken from that sheet music cover illustrated by William Spalding.
Surfers are welcome to contribute any further information about this performer.